Electrical properties, the conductivity and permittivity of tissue, are quantities that describe the interaction of an object and electromagnetic fields. These properties influence electromagnetic fields and are influenced themselves by physiological phe- nomena such as lesions or a stroke. Therefore, they are important in identifying or diagnosing the severity of pathologies, and they are essential in magnetic resonance imaging (MRI) safety and efficiency by determining tissue heating or sensitivity to excitation pulses and antenna designs. In two-dimensional electromagnetic fields, which occur in specific measurement geometries, it is possible to simplify the relationship between electromagnetic fields and electrical properties, and reconstruct these properties using essentially a forward operation, foregoing a full inversion scheme. These insights also help to find, and ex- plain, the cause of specific artefacts, such as those caused by mismatches in incident field used in the computation of the full electromagnetic fields. The two-dimensional field assumption necessary for the simplified relationship described above is subsequently tested, and it is shown that this assumption does not hold when the object is sufficiently translation variant in the longitudinal direction. That is, even if the fields for a translation invariant object would be two-dimensional, they become three-dimensional through the interaction of the tissue parameters with the fields, which cause out of plane current and field contributions. Another interesting application of closed form expressions between currents and fields is the target field method, which solves the inverse source problem between electric currents and static magnetic fields in a regularised manner by constraining their relationship to a cylindrical geometry. This method is adapted for transverse oriented magnetic fields to be used with Halbach type magnet arrays, and an open source tool is developed to make the method easy to apply for various design con- siderations. Moving away from constraints on the field or current structure, we show the intri- cate relationship between electrical properties and the measured signal in an MRI scanner. This is done by deriving the electro- (and magneto-) motive force for a typ- ical MRI scenario without any assumptions on the object or electro-magnetic fields. This model can then even be used to reconstruct electrical properties from the sim- plest MRI signal, namely the free induced decay (FID) signal. To round off our investigation of tissue properties we take a small detour to the magnetic tissue property, the permeability or magnetic susceptibility. For reconstruct- ing this tissue property a dipole deconvolution is required, where the dipole convolu- tion loses information of the original object through the zeros of the dipole kernel. A new machine learning based approach to reconstruct the lost information is investi- gated in the final chapter of this thesis.@en